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* @license Apache-2.0
*
* Copyright (c) 2018 The Stdlib Authors.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
'use strict';
// MODULES //
var isnan = require( '@stdlib/math/base/assert/is-nan' );
var beta = require( '@stdlib/math/base/special/beta' );
var pow = require( '@stdlib/math/base/special/pow' );
// MAIN //
/**
* Returns the skewness of a Kumaraswamy's double bounded distribution.
*
* @param {PositiveNumber} a - first shape parameter
* @param {PositiveNumber} b - second shape parameter
* @returns {number} skewness
*
* @example
* var v = skewness( 0.5, 1.0 );
* // returns ~0.639
*
* @example
* var v = skewness( 4.0, 12.0 );
* // returns ~-0.201
*
* @example
* var v = skewness( 12.0, 2.0 );
* // returns ~-1.2
*
* @example
* var v = skewness( 1.0, -0.1 );
* // returns NaN
*
* @example
* var v = skewness( -0.1, 1.0 );
* // returns NaN
*
* @example
* var v = skewness( 2.0, NaN );
* // returns NaN
*
* @example
* var v = skewness( NaN, 2.0 );
* // returns NaN
*/
function skewness( a, b ) {
var sigma2;
var m1;
var m2;
var m3;
if (
isnan( a ) ||
a <= 0.0 ||
isnan( b ) ||
b <= 0.0
) {
return NaN;
}
m1 = b * beta( 1.0 + ( 1.0/a ), b );
m2 = b * beta( 1.0 + ( 2.0/a ), b );
m3 = b * beta( 1.0 + ( 3.0/a ), b );
sigma2 = m2 - ( m1*m1 );
return ( m3 - ( 3.0*m1*sigma2 ) - ( m1*m1*m1 ) ) / pow( sigma2, 1.5 );
}
// EXPORTS //
module.exports = skewness;
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